Cohomology of parallelized n-manifolds carries a natural homotopy involutive n-Frobenius structure extending the rational homotopy type, via Quillen equivalence to n-Poisson cooperad comodules.
Models for configuration spaces of points via obstruction theory I
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An explicit A_infinity description of the Hochschild homology transfer yields a rational model for the Becker-Gottlieb transfer and proves vanishing of certain rational characteristic classes for manifold bundles while modeling fiberwise THH-simple structures.
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Homotopy Frobenius structures on the cohomology of a manifold
Cohomology of parallelized n-manifolds carries a natural homotopy involutive n-Frobenius structure extending the rational homotopy type, via Quillen equivalence to n-Poisson cooperad comodules.
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A rational model for the fiberwise THH transfer II: $A_\infty$-algebras
An explicit A_infinity description of the Hochschild homology transfer yields a rational model for the Becker-Gottlieb transfer and proves vanishing of certain rational characteristic classes for manifold bundles while modeling fiberwise THH-simple structures.